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In this passage, Benjamin Banneker presents an argument to Thomas Jefferson that defends the rights of slaves. He argues that the ideas that Jefferson stated in the Declaration of Independence are against those that defend slavery. He does so by using several rhetorical strategies, such as ethos, pathos and logos.
Banneker employs ethos, an appeal to authority, when he tells Jefferson that he belongs to the same type of people who are held in slavery. He refers to them as "my brethren," and shows that he knows their situation very well, making him someone worth listening to.
Banneker also employs pathos when he appeals to the emotions of Jefferson. He does so when encouraging Jefferson to think of the feelings that guided him to write the Declaration of Independence and to seek the independence of the colonies.
Finally, Banneker uses logos throughout the text as he points out the contradictions found in Jefferson's opinions. In particular, he contrasts Jefferson's defense of liberty with his position on the subject of slavery.